The Kodaira-Spencer map for nondegenerate toric hypersurfaces

Abstract

In this article we vary f over all nondegenerate Laurent polynomials with fixed 3-dimensional Newton polytope. Choosing an appropriate surrounding toric variety we get a family of minimal models of surfaces in a toric 3-fold. We compute the number of moduli of such a family. We illustrate our results at some examples of surfaces of general type.